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Titlebook: Optimization and Dynamical Systems; Uwe Helmke,John B. Moore Book 1994 Springer-Verlag London 1994 Dynamical System.Dynamische Systeme.Kon

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书目名称Optimization and Dynamical Systems
编辑Uwe Helmke,John B. Moore
视频video
丛书名称Communications and Control Engineering
图书封面Titlebook: Optimization and Dynamical Systems;  Uwe Helmke,John B. Moore Book 1994 Springer-Verlag London 1994 Dynamical System.Dynamische Systeme.Kon
描述This work is aimed at mathematics and engineering graduate students and researchers in the areas of optimization, dynamical systems, control sys­ tems, signal processing, and linear algebra. The motivation for the results developed here arises from advanced engineering applications and the emer­ gence of highly parallel computing machines for tackling such applications. The problems solved are those of linear algebra and linear systems the­ ory, and include such topics as diagonalizing a symmetric matrix, singular value decomposition, balanced realizations, linear programming, sensitivity minimization, and eigenvalue assignment by feedback control. The tools are those, not only of linear algebra and systems theory, but also of differential geometry. The problems are solved via dynamical sys­ tems implementation, either in continuous time or discrete time , which is ideally suited to distributed parallel processing. The problems tackled are indirectly or directly concerned with dynamical systems themselves, so there is feedback in that dynamical systems are used to understand and optimize dynamical systems. One key to the new research results has been the recent discovery of rather
出版日期Book 1994
关键词Dynamical System; Dynamische Systeme; Kontrolltheorie; Lyapunov stability; Numerische Lineare Algebra; Op
版次1
doihttps://doi.org/10.1007/978-1-4471-3467-1
isbn_softcover978-1-4471-3469-5
isbn_ebook978-1-4471-3467-1Series ISSN 0178-5354 Series E-ISSN 2197-7119
issn_series 0178-5354
copyrightSpringer-Verlag London 1994
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Matrix Eigenvalue Methods,bits from astronomical measurements. So we might ask: “What is new and of current interest in .” Our curiosity to investigate this question along the lines of this work was first aroused by the conjunction of two “events”.
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Linear Programming, symmetric matrix. Thus with a generic initial condition . (0) = .. where .. is real symmetric, . (.) converges to a diagonal matrix H., with its diagonal elements ordered according to the ordering in the prespecified diagonal matrix ..
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Singular Value Decomposition,Many numerical methods used in application areas such as signal processing, estimation, and control are based on the singular value decomposition (SVD) of matrices. The SVD is widely used in least squares estimation, systems approximations, and numerical linear algebra.
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Balanced Matrix Factorizations,The singular value decomposition of a finite-dimensional linear operator is a special case of the following more general matrix factorization problem: Given a matrix . ∈ .. find matrices . ∈ ℝ. and . ∈ ℝ. such that
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Matrix Eigenvalue Methods,bits from astronomical measurements. So we might ask: “What is new and of current interest in .” Our curiosity to investigate this question along the lines of this work was first aroused by the conjunction of two “events”.
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Double Bracket Isospectral Flows,he ordinary differential equation . where [.] = . denotes the Lie bracket for square matrices and . is an arbitrary real symmetric matrix. We term this the . equation. Brockett proves that (1.1) defines an isospectral flow which, under suitable assumptions on ., diagonalizes any symmetric matrix . (
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